Pascal\'s triangle using Python-full source code

What is a Pascal\’s Triangle?

Pascal\’s triangle is a triangular array of numbers that starts with

1 at the top and has each subsequent row constructed by adding the two numbers diagonally above it. Each number in the triangle represents the sum of the two numbers directly above it. The first few rows of :

Pascal\’s triangle has many interesting properties and applications in mathematics, including its use in calculating binomial coefficients and the expansion of powers of binomials.

Properties of pascal\’s triangle

Pascal\’s triangle has several interesting properties, including:

Each number in the triangle is the sum of the two numbers diagonally above it.
The sum of the numbers in each row of the triangle is equal to 2 to the power of the row number.
The sum of the numbers in each diagonal of the triangle is equal to the corresponding Fibonacci number sequence.
The triangle contains many patterns, including the triangular numbers, tetrahedral numbers, and the Fibonacci sequence.
The nth row of Pascal\’s triangle represents the coefficients of the expansion of (a + b)^n.
Pascal\’s triangle has connections to probability theory, number theory, algebra, and combinatorics.
Pascal\’s triangle can be extended to include negative numbers and fractions, and has applications in advanced mathematics and physics, including quantum mechanics and string theory.

These are just a few of the many interesting properties of Pascal\’s triangle.

Python Code

def pascal_triangle(n):
triangle = [[1]]
for i in range(1, n):
prev_row = triangle[i-1]
row = [1]
for j in range(1, i):
row.append(prev_row[j-1] + prev_row[j])
row.append(1)
triangle.append(row)
return triangle

#Print out the first 10 rows of Pascal\’s triangle

for row in pascal_triangle(10):
print(row)

This code defines a function pascal_triangle that takes an integer n as input and returns a list of lists representing the first n rows of Pascal\’s triangle.

The function starts with the first row of the triangle, which is just [1]. It then iterates from the second row to the nth row, generating each row by adding the two numbers diagonally above it in the previous row.

The resulting triangle list of lists is then printed out row by row using a for loop.

I hope this helps! Let me know if you have any other questions.